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Introduction to Information Visualisation by Riccardo Mazza University of Lugano Faculty of Communication Sciences March 2004
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Page 1: Mazza introduction-to-information-visualization-2004

Introduction to Information

Visualisation

byRiccardo Mazza

University of LuganoFaculty of Communication Sciences

March 2004

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This document was produced with LYX and LATEX on GNU/Linux.The versioning has been managed with CVS.

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1 Introduction

There are several situations in the real world where we try to understand some phenomena, data,and events by graphics. Some aspects, such as when people need to find a route on a city map,the stock market trends during some period, the unemployment diffusion in Europe, etc. may beunderstood better using graphics rather than text (Ruddle et al., 2002). Let us consider for examplea situation when a person needs to find a route to go from Lugano to Pisa. This information canbe represented both in a pictorial way, such as a map, and in a textual way, such as the textualdescription of a route. See this example represented in Figure 1.

Some specific aspect that may be interesting when one is finding a route, such as the possibilityfor finding an alternative route, or the existence of historical places in the vicinity of the route, maybe understood better from the graph rather then the textual format.

There are some specific aspects that may be understood better from graphics than from thetextual format, such as the possibility for finding an alternative route, or the existence of historicalplaces in the vicinity of the route. Graphics, if well constructed, may make the human cognitiveprocess of constructing a mental image of the route easier (Ruddle et al., 2002).

1.1 Graphics for presentation

Graphics are a mean to display facts about the data in a way that others can see and understandthe underlying structure and the hypothesis about the data (Rober, 2000). Tufte (1983, p. 13)writes, “graphical excellence consists of complex ideas communicated with clarity, precision, andefficiency”. See for instance Figure 2. This map by Charles Joseph Minard portrays the lossessuffered by Napoleon’s army in the Russian campaign of 1812. Beginning at the Polish-Russianborder, the thick band shows the size of the army at each position. The path of the Napoleon’sretreat from Moscow in the bitterly cold winter is depicted by the dark lower band, which is tiedto temperature and time scales. Edward Tufte, a highly reputed visual designer, statistician andacademic, comments on this image “ It may well be the best statistical graphic ever drawn” (Tufte,1983, p. 40 ).

1.2 Graphics for explorative analysis

Graphics also are a mean for finding and identifying structures and properties in a given data set(Card et al., 1999; Tufte, 1983; Rober, 2000). The special properties of visual perception of datamay facilitate the finding of relationships, trends, revealing hidden patterns, or as Bertin (1981, p.16) says, “it is the visual means of resolving logical problems”. To illustrate, Figure 3 represents amap of London’s Soho district were an outbreak of cholera appeared in 1845. Black dots representindividual deaths from cholera, and x marks the position of the water pumps. This map allowedDr. John Snow to observe that most of the deaths of the area were concentrated around the Broad

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Figure 1: Driving directions from Lugano to Pisa provided both in graphical and textual format.Images from http://www.viamichelin.com

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Figure 2: The Napoleon’s army route in the Russian campaign of 1812 by Charles J. Minard, takenfrom Tufte (1983).

Street water pumps, which was discovered to be a cause of the diffusion of cholera in the area.(Tufte, 1983; Spence, 2001).

1.3 Graphics for confirmative analysis

Graphics are also the visual mean to confirm or reject some hypothesis about the data. For ex-ample, operators in the stock market exchange know that stock market indexes between differentcountries influence each other. This can be illustrated by the picture in Figure 4 representing thevalues of MibTel, the Italian stock market index and the US Down Jones market index withinone year. It is easy to recognise that the increasing and decreasing values of both indexes cometogether. This relation, explicitly presented in the graphics, would be represented in the textualrepresentation of the values by symbolic formulas which are less expressive and intuitive that apicture (Larkin and Simon, 1987).

2 Information Visualisation

Graphical representations are often referred by eminent authors with the term “visualisation” (orvisualization in the more diffused American version of the term). For instance, Card et al. (1999,p. 6) define the term visualisation as “the use of computer-supported, interactive, visual represen-

tations of data to amplify cognition”. It has been noted by Spence (2001) that there is a diversityof uses of the term “visualisation”. For instance, in a dictionary the following definitions can be

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Figure 3: An 1845 map of London’s Soho district plotted by Dr. John Snow showing deaths fromCholera and the location of water pumps. Dots represent cholera cases and X represent waterpumps. Image from Tufte (1983).

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Figure 4: A comparison chart between the Italian stock market index, MibTel (in blue) and theUnited States’ Down Jones market index (in red). Taken from http://www.borsanalisi.com

found:

Visualize: form a mental image of .. 1.

Visualization: The display of data with the aim of maximizing comprehension rather

than photographic realism2.

Visualization: the act or process of interpreting in visual terms or of putting into

visible form3

These definitions reveal that visualisation is an activity in which humans are engaged, as an in-ternal construct of the mind (Spence, 2001; Ware, 2000). It is something that cannot be printedon a paper or displayed on a computer screen. With these considerations we can summarise thatvisualisation is a cognitive activity, facilitated by graphical external representations from whichpeople construct internal mental representation of the world (Ruddle et al., 2002; Spence, 2001;Ware, 2000). Computers may facilitate the visualisation process with some visualisation tools.This is especially true in the latest years with the use of more and more powerful computers atlow cost. However, the above definition is independent from computers: although computers canfacilitate visualisation, it still remains an activity that happens in the mind. Some authors use theterm “visualisation” to refer to both the printed graphical representation and the cognitive process

1The Concise Oxford Dictionary. Ed. Judy Pearsall. Oxford University Press, 2001. Oxford Reference Online.Oxford University Press.

2A Dictionary of Computing. Oxford University Press, 1996. Oxford Reference Online. Oxford University Press.3Merriam-Webster Online dictionary http://www.webster.com

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of understanding an image. In this thesis, we maintain the distinction between the creation of apictorial representation of some data and the formation of an internal mental model of the datawhen interpreting the pictorial representation.

Information Visualisation is a relatively new discipline concerned with the creation of visualartefacts aimed at amplifying cognition. A number of new definitions have been produced todefine the scope of this discipline. The Information Visualisation Research Group at the Institutefor Software Research at University of California, Irvine cite on its Web pages:

Information visualization focuses on the development and empirical analysis of meth-

ods for presenting abstract information in visual form. The visual display of infor-mation allows people to become more easily aware of essential facts, to quickly see

regularities and outliers in data, and therefore to develop a deeper understandingof data. Interactive visualization additionally takes advantage of people’s ability to

also identify interesting facts when the visual display changes, and allows them tomanipulate the visualization or the underlying data to explore such changes4 .

Similarly, the User Interface Research Group Web-site of the Palo Alto Research Centre (PARC-XEROX) defines that:

Information Visualization is the use of computer-supported interactive visual rep-resentations of abstract data to amplify cognition. Whereas scientific visualization

usually starts with a natural physical representation, Information Visualization ap-plies visual processing to abstract information. This area arises because of trends

in technology and information scale. Technically, there has been great progress inhigh-performance, affordable computer graphics. At the same time, there has been a

rapid expansion in on-line information, creating a need for computer-aid in findingand understanding them. Information Visualization is a form of external cognition,

using resources in the world outside the mind to amplify what the mind can do5.

The above definition is appropriate nowadays with the computers being a constant part of our life,but as Spence (2001) and Hearst (2003) pointed out the role of computers is merely of a mean thatfacilitates visualisations. Hearst (2003) summarises that IV is:

The depiction of information using spatial or graphical representations, to facilitate

comparison, pattern recognition, change detection, and other cognitive skills by mak-ing use of the visual system.

4http://www.isr.uci.edu/research-visualization.html5http://www2.parc.com/istl/projects/uir/projects/ii.html

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IV has a long history having its origin from the historical works of J. H. Lambert [1728-1777]and William Playfair [1759-1823] who were the first to introduce graphics, in contrast with thetabular presentation of data and are considered the inventors of the modern graphics design (Tufte,1983). Starting with Playfair, data were represented with methods of plotting. Other importantcontributions were made more recently by Jacques Bertin and Edward Tufte. Bertin, a Frenchcartographer, was the first who tried to define, in 1967, a theory of IV by the identification of thebasic elements of diagrams and described a framework for graphics design (Bertin, 1983). In 1983Tufte published his theory of data graphics focused on the maximisation of the density of usefulinformation in graphics (Tufte, 1983). Both Bertin and Tufte’s theories have influenced the currentdevelopment of IV.

2.1 Cognitive amplification

Graphics aid thinking and reasoning in several ways. For example, let us take a multiplication (atypical mental activity) e.g. 27 � 42 in our head, without having a pencil and paper. This willtake usually at least five times longer than when using a pencil and paper (Card et al., 1999). Thedifficulty in doing this operation in the mind is holding the partial results of the multiplication inthe memory until they can be used:

2 7 x4 2

5 41 0 8 -

1 1 3 4

This is an example which shows how visual and manipulative use of the external represen-tations and processing amplifies cognitive performance. Graphics use the visual representationsthat help to amplify cognition. They convey information to our minds that allows us to search forpatterns, recognise relationship between data and perform some inferences more easily. Card et al.(1999) propose six major ways in which visualisations can amplify cognition:

1. by increasing the memory and processing resources available to users;

2. by reducing the search for information;

3. by using visual representations to enhance the detection of patterns;

4. by enabling perceptual inference operations;

5. by using perceptual perception mechanisms for monitoring;

6. by encoding information in a manipulable medium.

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IV is becoming an increasingly important discipline because the availability of powerful represen-tations may facilitate the way we present and understand large complex dataset. Larkin and Simon(1987) argued in their seminal paper “Why a diagram is (sometimes) worth ten thousand words”that the effectiveness of graphical representations is due to their spatial clarity. Larkin and Simoncompared the computational efficiency of diagrams and sentences in solving Physics problems,and concluded that diagrams helped in three basic ways:

1. Locality - is enabled by grouping together information that is used together. This avoidslarge amounts of search and allows different information closely located to be processedsimultaneously. For example, Figure 4 puts together information about the history of twodifferent stock market indexes and allows to process their evolution immediately.

2. Minimising labelling - is enabled by using location to group information about a singleelement, avoiding the need to match symbolic labels and leading to reducing the workingmemory load. For example, driving directions from Lugano to Pisa provided in graphicalformat in Figure 1 use visual entities such as lines depicted in red with a yellow stripe in themiddle to denote a highway. Turning points (such as in Parma in the example) are clearlyindicated by a crossing of the roads. Symbolic textual representations used in the textualformat of the map are unnecessary because the connections are explicitly represented in thegraphics.

3. Perceptual enhancement - is enabled by supporting a large number of perceptual infer-ences which are easy for humans to perform. For example, in Figure 3 the link betweendeaths from cholera and the location of a water pump responsible for the spread of choleracould be recognised immediately.

IV definitions introduce the term “abstract data”, for which some clarification is needed. Thedata itself can have a wide variety of forms, but one can distinguish between data that have aphysical correspondence and is closely related to mathematical structures and models (e.g. theairflow around the wing of an aeroplane, or the density of the Ozone layer surrounding earth)and data that is more abstract in nature (e.g. the stock market fluctuations, or the effects of tem-perature on the Napoleon’s army movements in the Russian campaign). The former is known asScientific Visualisation, and the latter as Information Visualisation. (Spence, 2001; Uther, 2001;Hermann et al., 2000). Scientific Visualisation was developed in response to the needs of scien-tists and engineers to view experimental or phenomenal data in graphical formats (examples aregiven in Figure 5), while Information Visualisation is dealing with unstructured data sets as a dis-tinct flavour (Hermann et al., 2000). This thesis deals with Information Visualisation, and henceScientific Visualisation is beyond the scope of this review.

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Figure 5: Two examples of scientific visualisations. On the left, representation of thelaminar flows on the wing profile (image taken from http://www.esa.int/export/esaMI/High_School/ESAF8BG18ZC_1.html). On the right, Ozone hole over the SouthPole during September 2001 (image taken from http://www.esa.int/export/esaSA/ESALRRVTYWC_earth_1.html)

A key question in IV is how we convert abstract data into a graphical representation, preservingthe underlying meaning and, at the same time, providing new insight (Hearst, 2003). There isno “magic formula” that helps the researchers to build systematically a graphical representationstarting from a raw set of data. It depends on the nature of the data, the type of information to berepresented and its use, but more consistently, it depends on the creativity of the designer of thegraphical representation. Some interesting ideas, even if innovative, have often failed in practice.Tufte (1983) and Bertin (1981) list a number of examples of graphics that distort the underlyingdata or communicate incorrect ideas. Tufte indicates some principles that should be followed tobuild effective well designed graphics. In particular, a graphic should:

� show the data;

� avoid distorting what the data have to say;

� present many data in a small space;

� make large data sets coherently;

� encourage inferential processes, such as comparing different pieces of data;

� give different perspectives on the data - from broad overview to the fine structure.

Graphics facilitate IV, but a number of issues must be considered (Shneiderman, 2002; Tufte,1983; Spence, 2001):

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Data Tables Visual Struc-tures

Views Human inter-action

Tasks Level

Spatial (scien-tific)GeographicDocumentsTimeHierarchiesNetworks

World Wide

Web

PositionMarksProprieties:-Connection-Enclosure-Retinal-Time

Axes:-Composition-Alighment-Folding-Recursion

-Overloading

BrushingZoomingOverview+ de-tail

Focus+context

DynamicqueriesDirect Manipu-lation

Magic lenses

OverviewZoomFilterDetails-on-demandBrowseSearchRead factRead compari-sonRead patternManipulate

Create

DeleteReorderClusterClassPromoteAverageAbstractInstantiateExtractCompose

Organize

Table 1: Specific techniques for Information Visualisation identified by Card et al. (1999)

1. Data is nearly always multidimensional, while graphics represented on a computer screenor on a paper are presented in a 2D dimensional surface;

2. Sometimes we need to represent a huge dataset, while the number of data representable ona computer screen or on a paper is limited;

3. Data may vary during the time, while graphics are static;

4. Humans have remarkable abilities to select, manipulate and rearrange data, so the graphicalrepresentations should provide users with these features.

The above issues are considered in the IV field, and a number of methods and techniques havebeen proposed to meet these requirements. Card et al. (1999, p.33) give a comprehensive list ofeight types of data, eleven visual structures, four views, three types of human interaction, eleventasks and eleven levels that a user might want to accomplish with a visualisation tool (see Table 1).This is a multitude of possibilities. Next sections will describe some techniques that can be usedto display pictorial representations and that could be (or have already been) considered to displaystudents’ data in educational environments.

2.2 Issues to consider in Information Visualisation

Before using one or more IV techniques we have to consider several issues (Spence, 2001; Cardet al., 1999; Hearst, 2003; Reed and Heller, 1997):

1. The problem. This relates to what has to be presented, found, or demonstrated.

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2. The nature of the data. Data types could be numerical (e.g. list of integers or reals),ordinal (non-numerical data having a conventional ordering, such as days of the week), andcategorical (data with no order, such as names of persons or cities).

3. Number of data dimensions. Depending on the number of dimensions (also called at-tributes or variables (Spence, 2001)), representations are said to be handling univariate

(one dimension), bivariate (two dimensions), trivariate (three dimensions), and multivari-ate (four or more dimensions) data. We perceive our world in three spatial dimensions, so itis easy to map and interpret up to three dimensions. However, handling more than three di-mensions is very frequent in real world situations and represents one of the most challengingtasks in IV.

4. Structure of the data. This could be linear (data coded in plain data structures such asarrays, tables, alphabetical lists, sets, etc.), temporal (data which changes during the time),spatial or geographic (data which has a correspondence with something physical, e.g. maps,floor plans, 3D CAD; usually this is a subject of scientific visualisation and is not consid-ered to be IV in the strict sense), hierarchical (data that naturally arise in taxonomies, thestructures of organisations, disk space management, genealogies, etc. ), network (data de-scribing graph structures, i.e. nodes and links, nodes representing a data point, and a linkrepresenting a relationship between two nodes).

5. Type of interaction. Whether the resulting graphical representation is static (e.g. a printor a static image on a display screen), transformable (users can manipulate how the rep-resentation is rendered, such as zooming or filtering), or manipulable (users may controlparameters during the process of image generation, i.e. restricting the view to certain dataranges)

Each one of the previous can suggest the use of one or more techniques, the most important (andused) ones are outlined next.

2.3 Techniques for representing univariate and bivariate linear data

Univariate and bivariate linear data are easily representable as a single image which relates datavalues with some scale in a plain. Conventional approaches are scatterplots, charts, and his-

tograms. When used with bivariate data, scatterplots are helpful for encouraging the viewer toassess the possible causal relationship between the two plotted variables (Tufte, 1983). Figure 6on the left represents a one-dimensional scatterplot illustrating the prices of some cars. The onlyattribute here is represented by the numeric value of a car, mapped onto the scale of the axes.This image could be helpful to easily locate the lowest, the highest values, and the general dis-tribution of values and brunching on data (Spence, 2001). Figure 6 in the middle represents a

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Figure 6: Samples of 1D (left), 2D (middle) scatterplots, and histogram . Images from Spence(2001) (left and middle images) and http://www.physics.umass.edu/p151sec2s02/(right image).

two-dimensional scatterplot which relates prices of houses with the number of bedrooms from ahouse-hunting archive. Users can clearly identify global trends (price of houses increases withthe number of bedrooms), as well as items far from other having similar characteristics (e.g. aone-bedroom house selling for more than 250.000 GBP) (Spence, 2001). Another form of rep-resentation is the histogram (Figure 6, right). The example reports distribution of scores on aPhysics exam. Histograms are suitable to facilitate comparisons between the values of a dimen-sion, while scatterplots are helpful to convey overall impression of relationships between twovariables (Hearst, 2003).

2.4 Techniques for representing trivariate linear data

Three-dimensional linear data is easily representable in a three dimensional space, as we are livingin a three-dimensional world. However, the problem still arises because we basically can representin a printed image or on a computer screen a two dimensional representation of a three-dimensionalspace, hence some approximations are necessary (Spence, 2001). Figure 7 left illustrates an ex-ample of a 3 dimensional scatterplot were each dimension is linearly mapped on an axis. Theimpassable barrier of the 2D image makes impossible to distinguish between the number of bed-rooms of C and B. To overcome this problem some solutions have been proposed, such as toproject items on the plans to identify the exact position (see Figure 7, centre) or to replace onedimension with a different shape of the items according to this value (see Figure 7, right).

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Figure 7: Some examples of 3D scatterplots. Images from Spence (2001) (left), http://www.nhm.ac.uk/entomology/bombus/introduction.html(centre), http://www.kovcomp.co.uk/xlstat/tools/t01.html(right).

2.5 Techniques for representing multivariate linear data

Very often real world cases cope with situations where relationships between more than threevariables must be analysed. Let’s think about an analysis of factors such as age, living place, job,and sex on the appearance of cancer on a sample of patients. This is a challenging aspect in IV,because some proprieties of images have to be explored to distinguish between several variables ina 2D drawing plane. For this purpose several methods have been proposed. Sachinopoulou (2001)suggested a classification into six groups, summarised in the following table:

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Methods Description Some known techniques

Geometric Transforming and projecting data in a geomet-ric space.

Scatterplot matrix, Hyperslice,Prosection views, Surface andvolume plots, Parallel coordi-nates, Textures and rasters.

Icon Relies on a geometric figure (the icon) wherethe values of an attribute is associated with onefeatures of this, such as the colour, a shape, theorientation.

Chernoff faces, Stick figure,Colour icon, Glyphs and Auto-glyph.

Pixel Use pixel as basic representation unit, and ma-nipulate pixels to represent data.

Space fillings and Mosaic plots.

Hierarchical Include trees and hierarchies and are usefulwhen the data has some hierarchical or net-work structure.

Hierarchical axes, Dimensionstacking, Threes, Worlds withinworlds, Infocube.

Distorsion Propose to distort the tree-dimensional spaceto allow more information to be visualised.

Perspective Wall, Pivot tableand table lens, Fish eye view,Hyperbolic trees, Hyperbox.

Graph based Represent data using nods and edges and isadopted when the large graphs should be rep-resented.

Basic graph, Hyperbolic graph.

Techniques cited in the rightmost column of the table above are described in details in Sachinopoulou(2001); Card et al. (1999); Spence (2001); Chen (1999). These techniques are able to representdata in multidimensional space. A comprehensive description of multidimensional techniques isbeyond the scope of this work, rather we focus on those techniques that have been used in Cour-seVis.

A number of additional techniques for multidimensional data representations exist. Differentlyfrom the techniques cited in the table above, they don’t offer the possibility to establish relationshipbetween each variable, but may represent several attributes allowing relationships on a subset ofvariables. Some of them are composition, layering and separation, micro-macro readings, andsmall multiplies.

Composition

The basic idea of the composition technique (Mackinlay, 1986; Card et al., 1999) is the orthogonalplacement of axes that encode the same information, creating a 2D metric space of multidimen-sional data. An example of this technique is the diagram of the Napoleon’s army route in Figure 2.This is an example of single-axis composition technique (Mackinlay, 1986) where attributes armysize, army longitude, army latitude, and temperature have identical horizontal axis which is thetime. Figure 8 illustrates how C. J. Minard composed these variables in the famous diagram.

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Figure 8: Single-axis composition technique used by C. J. Minard in the Napoleon’s army routein the Russian campaign diagram. Image from Mackinlay (2000).

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Layering and separation

Layering and separation is a technique illustrated, among others, by Tufte (1990) and concerns thevisual differentiation of various aspects of the data. Tufte argues that “confusion and clutter arefailure of the design, not attributes of information ... the point is to find design strategies that revealdetail and complexity - rather than to fault the data for an excess of complication” (Tufte, 1990,p. 53). He proposes layering and separation as one of the most powerful devices for reducingnoise and enriching the content in graphics, and is achieved by distinction of colour, shape, size,addition of elements that direct the attention via visual signals, or ordering data to emphasise layerdifferences (Ruddle et al., 2002). An example of this technique is visible in Figure 9. It shows acity map of the centre of Florence. This picture illustrates at least 2 layers of reading: the locationof historical places and the map of the streets to find a path. Colours have been used to distinguishbetween parks (in green), interesting places for tourists (brown), river (blue), and major streets(yellow). Shapes have been used to direct attention of tourists in historical places, and give an ideaabout what sort of building it is. This map can be used also by someone who is not interested inhistorical monuments in Florence but has to find the route to move from the train station to Piazza

Signoria.

Micro-macro readings

Micro-macro reading “is a method for presenting large quantities of data at high densities in a

way that a broad overview of the data is given and yet immense amount of detail is provided”(Ruddle et al., 2002). It encodes information at different levels of detail, such as the same imagecan be used to detect fine-grained level on information encoded (micro processing) as well aslarge-grained level of information (macro processing). An example of micro-macro reading isdepicted in Figure 10. Here the picture allow the comparison of between-cycle variation (macro)and within-cycle variation (micro). Also shows an apparent growth trend in the wingspan of recentcycles (Tufte, 1990).

Small multiples

Small multiples technique consists of the same graphical design structure repeated several times(Tufte, 1983). It is used to compare at a glance series of graphics showing the same combinationof variables while another variable changes. This method considers positioning similar graphicalelements together in order to emphasise changes of the data (Ruddle et al., 2002). Figure 11illustrates a small multiples design for representing the coverage of mobile phones in Switzerlandfor the tree main operators. Comparisons are possible to decide which operator utilises on aspecific region for best signal reception.

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Figure 9: A city map of the centre of Florence, streets and historical places are encoded withdifferent shapes and colours. Image from http://www.hotelitaliani.it/Mappa/Informazioni/PiantinaFirenze.htm.

Figure 10: Diagram representing sunspots from 1880 to 1980 with the sine of the latitude mark-ing a sunspot placement. Micro-macro readings allow combining patterns, details, average andvariations with the same image. The lower time-series shows the total area of the sun’s surfacecovered by sunspots by summing over all latitudes. Diagram by David H. Hathaway, MarshallSpace Flight Centre, NASA, taken from Tufte (1990).

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Figure 11: Small multiples example. The coverage for mobile telephone network in Switzerlandbetween the tree operators: Swisscom (on the left), Orange (on the centre), and Sunrise (on right).

2.6 Techniques for representing spatial data

With the term spatial (or geographic) data we refer to representation techniques which have acorrespondence with something physical. For example, data maps (Tufte, 1983) represent one ormore attributes associated with areas of a map. See for instance the map in Figure 12 representingthe cancer mortality in the USA at Lung, Trachea, Bronchus and Pleura for white males in years1970 - 1994 in counties. Data maps can carry a huge volume of data in small space, but carryan intrinsic problem: they may give a wrong illusion that the importance of the information isgeographic, rather than factual (Ruddle et al., 2002; Tufte, 1983). For instance, the figure doesn’tallow ordering the counties according to the number of cancer deaths, or the number of peopleliving in the county.

Space-times narrative design is another technique for representing spatial data. Its basic ideais to add spatial dimensions to the design of the graphics, so that the data are moving over thespace as well as over the time (Tufte, 1983, 1990). The Napoleon’s army route in Figure 2 is anexcellent example. The graphics shows, among other things, how the crossing of the Berenzinariver caused lots of deaths on Napoleon’s troops, the latitude and longitude of movements, and thedirection of the movements. It depicts the dynamics of the whole march with a static image.

2.7 Techniques for representing hierarchical and network data

There are many situations where data to be represented is linked in a graph structure, for examplethe organisation chart in a company, pages in a Web site, or DNA sequences. This is often referredas network information visualisation, and involves gaining insight into a structure that may consistof many data items (Reed and Heller, 1997). These are usually graphically represented with adrawing graph. Graphs are sometimes problematic, because a graph with few nodes is easy todraw and to comprehend visually, but real world situations often need to handle large data sets.See for example Figure 13, where two examples of network drawing are depicted. The imageon the top is a representation of an intranet: the nodes are pages and links are URL connections

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Figure 12: A data map example. Cancer mortality in the USA years 1970 - 1994 - white males bycounty. Image from USA National Cancer Institute http://www3.cancer.gov/atlas/2.html.

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between pages. This network consists of 24 nodes easily represented in a 2D-picture. However,some situations have to deal with a large number of nodes. Figure 13 on the bottom representsan istance of a network with many nodes and links represented in a 3D picture. In this case, thelimitation of the design pane requires rendering the network as interactive graphs. By engagingtheir visual image, a user is able to navigate through large networks, and to explore different waysof arranging the network components on the screen.

2.8 View transformations

A problem humans are experiencing in their everyday life is to have too many things placed ina limited space: books on shelves, addresses in agenda, windows on a computer screen, data todisplay in a Personal Digital Assistant (PDA). The information explosion phenomena of last yearsleads to the existence of more data than what can easily be displayed at once. "Too much data, too

little display area" is a common problem in Information Visualisation (Spence, 2001). There areseveral techniques proposed to solve this problem, some of which are zooming, panning, scrolling,focus+context and magic lenses (Spence, 2001).

� Zooming is the increasing magnification of a decreasing (or increasing) fraction of a two-dimensional image.

� Panning is the smooth movement of a viewing frame over a two-dimensional image ofgreater size.

� Scrolling is the movement of data past a window able to contain only a part of it (such aswe are doing with the scrolling of a long document in a word processing program).

� Focus+context’s basic idea is to illustrate at the same time the overall picture (the context)and to see details of immediate interests (the focus). This technique allows users to ex-pand and contract selected sections of a large image, thereby displaying simultaneously thecontents of individual sections of a document as well as its overall structure.

� Magic lenses follow the metaphor of reading a text by the means of a lens that enlarges thesize of the text. In IV it can be used to place a lens upon the area of interest and receive moredetailed information on the data amplified with the lens. For instance, magic lenses couldbe applied to Figure 9: an application could show this map to tourists and a lens placed overparts of the map could show details about the historical place selected.

An example of zooming, scrolling, and panning is illustrated in Figure 14. Focus+context tech-nique is illustrated in an example in Figure 15. An example of magic lenses is illustrated in Figure16

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Figure 13: Two examples of network drawing. On the top, a graph of a small dimension intranet(image from Graphviz drawing software Web site: http://www.research.att.com/sw/tools/graphviz/examples/), on the bottom, a graph of some Internet Web sites (imagefrom TouchGraph drawing software Web site: http://www.touchgraph.com/bi.php?img=greenpeace_new.jpg).

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Figure 14: Zooming, scrolling, and panning operations from Descartes: a tool to support visualexploration of spatial data produced by Dialogis (http://www.dialogis.com). The middleof the right section of the window illustrates a schematic view of the entire territory. The frameshows the size and position of the territory fragment currently displayed in the map area relativeto the whole territory. Using the buttons at the top right (north,south, east, west) users can scrollthe territory shown in the map window.

Figure 15: The perspective wall invented by Mackinlay et al. (1991). It is a 2D layout wrappedaround a 3D structure, upon which label corresponds to files on the computer. Different la-bels denote different type of entities (folders, text files, wav, ...), located according to precisecriteria (date of creation of the file in x-axis and file type on y-axis). Image from http://www.inxight.com.

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Figure 16: The magic lenses techniques applied to the historical places in a city map of the centreof Florence. Image from http://www.hotelitaliani.it/Mappa/Informazioni/PiantinaFirenze.htm and modified

References

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